The angular impulsemomentum relation
Angular momentum
of a particle:
The symbol H_{O} denotes the angular
momentum and is defined as the moment of linear momentum around the point O, and given by the equation
Impulse of a
moment from time t_{1 }to t_{2}: The integral of the moment
over the time interval of concern is its impulse. The impulse of a moment is a
vector given by the integral

_{}
Moment and
rateofchangeof angular momentum relation: Starting from Newton’s second law,
calculating the moment of both sided of the equation with respect to a point O on an inertial frame results in
_{}
This
resulting relation between the moment and the rate of change of angular
momentum is called the momentrate of change of angular momentum relation
(MRCAM).
The angular
impulsemomentum relation: Integration of Newton’s 2^{nd} law over the time interval
from t_{1} to t_{2} results in
_{}
_{}
Therefore,
the angular momentum of a particle is changed by the impulse of the resultant
moment on the particle. There will be conservation
of angular momentum only if the impulse of the resultant moment is zero.
ã Mehrdad Negahban and the
University of Nebraska, 19962002.
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Department
of Engineering Mechanics, University of Nebraska, Lincoln, NE 685880526